
The reader should not confuse this VNR \(\Delta \)  with the standart notation of the lattice sphere packing density as in Section 1.2 of [1]}.
Using the union bound with the Theta series (see (REF )), the MLD probability of error
per lattice point of lattice \(\Lambda \)  can be bounded from above by [1]}
\(P_e(opt) \le P_e(ub),\) 
